- Author:
- Jagirhussan <r.jagir@auckland.ac.nz>
- Date:
- 2025-07-01 14:51:12+12:00
- Desc:
- Manuscript draft commit
- Permanent Source URI:
- https://staging.physiomeproject.org/workspace/d42/rawfile/7a829c334cfa12d90cc0f489f2ea7b6edd74ac9a/PulmonaryAcinusModel.cellml
<?xml version='1.0' encoding='UTF-8'?>
<model name="multi_compartment_acinus_model" xmlns="http://www.cellml.org/cellml/1.1#" xmlns:cellml="http://www.cellml.org/cellml/1.1#">
<units name="mole_per_litre">
<unit units="mole"/>
<unit exponent="-1" units="litre"/>
</units>
<units name="metre_cubed">
<unit exponent="3" units="metre"/>
</units>
<units name="m_cubed_per_s">
<unit exponent="3" units="metre"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mole_per_second">
<unit units="mole"/>
<unit exponent="-1" units="second"/>
</units>
<units name="mole_per_m_cubed">
<unit units="mole"/>
<unit exponent="-3" units="metre"/>
</units>
<units name="per_pascal">
<unit exponent="-1" units="pascal"/>
</units>
<units name="mol_per_L_Pa">
<unit units="mole"/>
<unit exponent="-1" units="litre"/>
<unit exponent="-1" units="pascal"/>
</units>
<units name="mol_per_Pa_s">
<unit units="mole"/>
<unit exponent="-1" units="pascal"/>
<unit exponent="-1" units="second"/>
</units>
<component name="Environment">
<variable name="time" public_interface="out" units="second"/>
<variable initial_value="101325" name="atm_pressure" public_interface="out" units="pascal"/>
<variable initial_value="6300" name="water_vapor_pressure" public_interface="out" units="pascal"/>
<variable name="P_atm_effective" public_interface="out" units="pascal"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P_atm_effective</ci>
<apply>
<minus/>
<ci>atm_pressure</ci>
<ci>water_vapor_pressure</ci>
</apply>
</apply>
</math>
</component>
<component name="breathing_waveform">
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.0004" name="tidal_volume" public_interface="out" units="metre_cubed"/>
<variable initial_value="0.2" name="breathing_frequency" public_interface="out" units="hertz"/>
<variable initial_value="0.4" name="inhale_fraction" units="dimensionless"/>
<variable name="Q_vent_total" public_interface="out" units="m_cubed_per_s"/>
<variable name="cycle_dur" units="second"/>
<variable name="t_mod" units="second"/>
<variable name="t_in" units="second"/>
<variable name="t_ex" units="second"/>
<variable initial_value="1" name="One" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>cycle_dur</ci>
<apply>
<divide/>
<ci>One</ci>
<ci>breathing_frequency</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>t_mod</ci>
<apply>
<minus/>
<ci>time</ci>
<apply>
<times/>
<ci>cycle_dur</ci>
<apply>
<floor/>
<apply>
<divide/>
<ci>time</ci>
<ci>cycle_dur</ci>
</apply>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>t_in</ci>
<apply>
<times/>
<ci>inhale_fraction</ci>
<ci>cycle_dur</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>t_ex</ci>
<apply>
<times/>
<apply>
<minus/>
<ci>One</ci>
<ci>inhale_fraction</ci>
</apply>
<ci>cycle_dur</ci>
</apply>
</apply>
<!--Inhalation-->
<!-- Exhalation phase-->
<apply>
<eq/>
<ci>Q_vent_total</ci>
<piecewise>
<piece>
<cn cellml:units="m_cubed_per_s">0</cn>
<apply>
<and/>
<apply>
<leq/>
<ci>breathing_frequency</ci>
<cn cellml:units="hertz">0</cn>
</apply>
<apply>
<leq/>
<ci>tidal_volume</ci>
<cn cellml:units="metre_cubed">0</cn>
</apply>
</apply>
</piece>
<piece>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<pi/>
<ci>tidal_volume</ci>
<ci>breathing_frequency</ci>
</apply>
<ci>inhale_fraction</ci>
</apply>
<apply>
<sin/>
<apply>
<times/>
<apply>
<divide/>
<ci>t_mod</ci>
<ci>t_in</ci>
</apply>
<pi/>
</apply>
</apply>
</apply>
<apply>
<lt/>
<ci>t_mod</ci>
<ci>t_in</ci>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<apply>
<divide/>
<apply>
<times/>
<apply>
<minus/>
<pi/>
</apply>
<ci>tidal_volume</ci>
<ci>breathing_frequency</ci>
</apply>
<apply>
<minus/>
<ci>One</ci>
<ci>inhale_fraction</ci>
</apply>
</apply>
<apply>
<sin/>
<apply>
<times/>
<apply>
<divide/>
<apply>
<minus/>
<ci>t_mod</ci>
<ci>t_in</ci>
</apply>
<ci>t_ex</ci>
</apply>
<pi/>
</apply>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<component name="ventilation_distributor">
<variable name="Q_vent_total" public_interface="in" units="m_cubed_per_s"/>
<variable initial_value="0" name="f_obs_1" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="f_obs_2" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="f_obs_3" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="f_obs_4" public_interface="out" units="dimensionless"/>
<variable initial_value="0" name="f_obs_5" public_interface="out" units="dimensionless"/>
<variable name="Q_A_1" public_interface="out" units="m_cubed_per_s"/>
<variable name="Q_A_2" public_interface="out" units="m_cubed_per_s"/>
<variable name="Q_A_3" public_interface="out" units="m_cubed_per_s"/>
<variable name="Q_A_4" public_interface="out" units="m_cubed_per_s"/>
<variable name="Q_A_5" public_interface="out" units="m_cubed_per_s"/>
<variable initial_value="0.000124" name="V0_1" public_interface="out" units="metre_cubed"/>
<variable initial_value="0.000124" name="V0_2" public_interface="out" units="metre_cubed"/>
<variable initial_value="0.000124" name="V0_3" public_interface="out" units="metre_cubed"/>
<variable initial_value="0.000124" name="V0_4" public_interface="out" units="metre_cubed"/>
<variable initial_value="0.000124" name="V0_5" public_interface="out" units="metre_cubed"/>
<variable initial_value="0.21" name="C_in_O2" public_interface="out" units="mole_per_m_cubed"/>
<variable initial_value="0.0004" name="C_in_CO2" public_interface="out" units="mole_per_m_cubed"/>
<variable name="sum_conductance" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>sum_conductance</ci>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<cn cellml:units="dimensionless">5</cn>
<ci>f_obs_1</ci>
</apply>
<ci>f_obs_2</ci>
</apply>
<ci>f_obs_3</ci>
</apply>
<ci>f_obs_4</ci>
</apply>
<ci>f_obs_5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_A_1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_vent_total</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs_1</ci>
</apply>
</apply>
<ci>sum_conductance</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_A_2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_vent_total</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs_2</ci>
</apply>
</apply>
<ci>sum_conductance</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_A_3</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_vent_total</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs_3</ci>
</apply>
</apply>
<ci>sum_conductance</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_A_4</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_vent_total</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs_4</ci>
</apply>
</apply>
<ci>sum_conductance</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_A_5</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_vent_total</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs_5</ci>
</apply>
</apply>
<ci>sum_conductance</ci>
</apply>
</apply>
</math>
</component>
<component name="perfusion_distributor">
<variable name="Q_blood_total" public_interface="in" units="m_cubed_per_s"/>
<variable initial_value="2666" name="P50" units="pascal"/>
<variable initial_value="2" name="n_hpv" units="dimensionless"/>
<variable initial_value="3e-10" name="k_ex_O2_1" public_interface="out" units="mol_per_Pa_s"/>
<variable initial_value="5e-09" name="k_ex_CO2_1" public_interface="out" units="mol_per_Pa_s"/>
<variable initial_value="3e-10" name="k_ex_O2_2" public_interface="out" units="mol_per_Pa_s"/>
<variable initial_value="5e-09" name="k_ex_CO2_2" public_interface="out" units="mol_per_Pa_s"/>
<variable initial_value="3e-10" name="k_ex_O2_3" public_interface="out" units="mol_per_Pa_s"/>
<variable initial_value="5e-09" name="k_ex_CO2_3" public_interface="out" units="mol_per_Pa_s"/>
<variable initial_value="3e-10" name="k_ex_O2_4" public_interface="out" units="mol_per_Pa_s"/>
<variable initial_value="5e-09" name="k_ex_CO2_4" public_interface="out" units="mol_per_Pa_s"/>
<variable initial_value="3e-10" name="k_ex_O2_5" public_interface="out" units="mol_per_Pa_s"/>
<variable initial_value="5e-09" name="k_ex_CO2_5" public_interface="out" units="mol_per_Pa_s"/>
<variable name="P_A_O2_1" public_interface="in" units="pascal"/>
<variable name="P_A_O2_2" public_interface="in" units="pascal"/>
<variable name="P_A_O2_3" public_interface="in" units="pascal"/>
<variable name="P_A_O2_4" public_interface="in" units="pascal"/>
<variable name="P_A_O2_5" public_interface="in" units="pascal"/>
<variable name="Q_b_1" public_interface="out" units="m_cubed_per_s"/>
<variable name="Q_b_2" public_interface="out" units="m_cubed_per_s"/>
<variable name="Q_b_3" public_interface="out" units="m_cubed_per_s"/>
<variable name="Q_b_4" public_interface="out" units="m_cubed_per_s"/>
<variable name="Q_b_5" public_interface="out" units="m_cubed_per_s"/>
<variable name="w1" units="dimensionless"/>
<variable name="w2" units="dimensionless"/>
<variable name="w3" units="dimensionless"/>
<variable name="w4" units="dimensionless"/>
<variable name="w5" units="dimensionless"/>
<variable name="w_sum" units="dimensionless"/>
<variable initial_value="1" name="One" units="dimensionless"/>
<variable initial_value="1e-06" name="theta" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>w1</ci>
<apply>
<divide/>
<ci>One</ci>
<apply>
<plus/>
<ci>One</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>P50</ci>
<apply>
<max/>
<ci>theta</ci>
<ci>P_A_O2_1</ci>
</apply>
</apply>
<ci>n_hpv</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>w2</ci>
<apply>
<divide/>
<ci>One</ci>
<apply>
<plus/>
<ci>One</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>P50</ci>
<apply>
<max/>
<ci>theta</ci>
<ci>P_A_O2_2</ci>
</apply>
</apply>
<ci>n_hpv</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>w3</ci>
<apply>
<divide/>
<ci>One</ci>
<apply>
<plus/>
<ci>One</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>P50</ci>
<apply>
<max/>
<ci>theta</ci>
<ci>P_A_O2_3</ci>
</apply>
</apply>
<ci>n_hpv</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>w4</ci>
<apply>
<divide/>
<ci>One</ci>
<apply>
<plus/>
<ci>One</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>P50</ci>
<apply>
<max/>
<ci>theta</ci>
<ci>P_A_O2_4</ci>
</apply>
</apply>
<ci>n_hpv</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>w5</ci>
<apply>
<divide/>
<ci>One</ci>
<apply>
<plus/>
<ci>One</ci>
<apply>
<power/>
<apply>
<divide/>
<ci>P50</ci>
<apply>
<max/>
<ci>theta</ci>
<ci>P_A_O2_5</ci>
</apply>
</apply>
<ci>n_hpv</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>w_sum</ci>
<apply>
<plus/>
<ci>w1</ci>
<ci>w2</ci>
<ci>w3</ci>
<ci>w4</ci>
<ci>w5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_b_1</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_blood_total</ci>
<ci>w1</ci>
</apply>
<ci>w_sum</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_b_2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_blood_total</ci>
<ci>w2</ci>
</apply>
<ci>w_sum</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_b_3</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_blood_total</ci>
<ci>w3</ci>
</apply>
<ci>w_sum</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_b_4</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_blood_total</ci>
<ci>w4</ci>
</apply>
<ci>w_sum</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>Q_b_5</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>Q_blood_total</ci>
<ci>w5</ci>
</apply>
<ci>w_sum</ci>
</apply>
</apply>
</math>
</component>
<component name="pulmonary_blood_pool">
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="0.05" name="V_b_pulm" public_interface="out" units="litre"/>
<variable initial_value="8.3e-05" name="Q_blood_total" public_interface="out" units="m_cubed_per_s"/>
<variable name="P_atm_effective" public_interface="in" units="pascal"/>
<variable name="C_sys_O2" public_interface="in" units="mole_per_litre"/>
<variable name="C_sys_CO2" public_interface="in" units="mole_per_litre"/>
<variable name="I_ex_O2_1" public_interface="in" units="mole_per_second"/>
<variable name="I_ex_O2_2" public_interface="in" units="mole_per_second"/>
<variable name="I_ex_O2_3" public_interface="in" units="mole_per_second"/>
<variable name="I_ex_O2_4" public_interface="in" units="mole_per_second"/>
<variable name="I_ex_O2_5" public_interface="in" units="mole_per_second"/>
<variable name="I_ex_CO2_1" public_interface="in" units="mole_per_second"/>
<variable name="I_ex_CO2_2" public_interface="in" units="mole_per_second"/>
<variable name="I_ex_CO2_3" public_interface="in" units="mole_per_second"/>
<variable name="I_ex_CO2_4" public_interface="in" units="mole_per_second"/>
<variable name="I_ex_CO2_5" public_interface="in" units="mole_per_second"/>
<variable initial_value="2666" name="P50" units="pascal"/>
<variable initial_value="2.7" name="n_hill" units="dimensionless"/>
<variable initial_value="0.0089" name="H_cap" units="mole_per_litre"/>
<variable initial_value="1.39e-06" name="alpha_O2" units="mol_per_L_Pa"/>
<variable initial_value="3.07e-05" name="alpha_CO2" units="mol_per_L_Pa"/>
<variable name="C_b_O2" public_interface="in" units="mole_per_litre"/>
<!--init: 0.0065, -->
<variable name="C_b_CO2" public_interface="in" units="mole_per_litre"/>
<!--init: 0.021,-->
<variable name="P_b_O2" public_interface="out" units="pascal"/>
<variable name="P_b_CO2" public_interface="out" units="pascal"/>
<variable name="I_ex_O2_total" units="mole_per_second"/>
<variable name="I_ex_CO2_total" units="mole_per_second"/>
<variable name="I_blood_O2" units="mole_per_second"/>
<variable name="I_blood_CO2" units="mole_per_second"/>
<variable name="dS_dp" units="per_pascal"/>
<variable name="cap_factor_O2" units="litre"/>
<variable name="cap_factor_CO2" units="litre"/>
<variable initial_value="1000" name="L_per_m_cubed" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>I_ex_O2_total</ci>
<apply>
<plus/>
<ci>I_ex_O2_1</ci>
<ci>I_ex_O2_2</ci>
<ci>I_ex_O2_3</ci>
<ci>I_ex_O2_4</ci>
<ci>I_ex_O2_5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_ex_CO2_total</ci>
<apply>
<plus/>
<ci>I_ex_CO2_1</ci>
<ci>I_ex_CO2_2</ci>
<ci>I_ex_CO2_3</ci>
<ci>I_ex_CO2_4</ci>
<ci>I_ex_CO2_5</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_b_O2</ci>
<apply>
<divide/>
<apply>
<minus/>
<ci>C_b_O2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>H_cap</ci>
<apply>
<power/>
<ci>P_b_O2</ci>
<ci>n_hill</ci>
</apply>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>P50</ci>
<ci>n_hill</ci>
</apply>
<apply>
<power/>
<ci>P_b_O2</ci>
<ci>n_hill</ci>
</apply>
</apply>
</apply>
</apply>
<ci>alpha_O2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_b_CO2</ci>
<apply>
<divide/>
<ci>C_b_CO2</ci>
<ci>alpha_CO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>dS_dp</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>n_hill</ci>
<apply>
<power/>
<ci>P_b_O2</ci>
<apply>
<minus/>
<ci>n_hill</ci>
<cn cellml:units="dimensionless">1</cn>
</apply>
</apply>
<apply>
<power/>
<ci>P50</ci>
<ci>n_hill</ci>
</apply>
</apply>
<apply>
<power/>
<apply>
<plus/>
<apply>
<power/>
<ci>P50</ci>
<ci>n_hill</ci>
</apply>
<apply>
<power/>
<ci>P_b_O2</ci>
<ci>n_hill</ci>
</apply>
</apply>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>cap_factor_O2</ci>
<apply>
<times/>
<ci>V_b_pulm</ci>
<apply>
<plus/>
<ci>alpha_O2</ci>
<apply>
<times/>
<ci>H_cap</ci>
<ci>dS_dp</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>cap_factor_CO2</ci>
<apply>
<times/>
<ci>V_b_pulm</ci>
<ci>alpha_CO2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_blood_O2</ci>
<apply>
<times/>
<ci>Q_blood_total</ci>
<ci>L_per_m_cubed</ci>
<apply>
<minus/>
<ci>C_sys_O2</ci>
<ci>C_b_O2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_blood_CO2</ci>
<apply>
<times/>
<ci>Q_blood_total</ci>
<ci>L_per_m_cubed</ci>
<apply>
<minus/>
<ci>C_sys_CO2</ci>
<ci>C_b_CO2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_b_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<ci>I_ex_O2_total</ci>
<ci>I_blood_O2</ci>
</apply>
<ci>cap_factor_O2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_b_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<plus/>
<apply>
<minus/>
<ci>I_ex_CO2_total</ci>
</apply>
<ci>I_blood_CO2</ci>
</apply>
<ci>cap_factor_CO2</ci>
</apply>
</apply>
</math>
</component>
<component name="systemic_circulation">
<variable name="time" public_interface="in" units="second"/>
<variable initial_value="60" name="tau_sys" public_interface="out" units="second"/>
<variable initial_value="0.00650022595698537" name="C_b_O2_init" public_interface="out" units="mole_per_litre"/>
<variable initial_value="0.0219998552095115" name="C_b_CO2_init" public_interface="out" units="mole_per_litre"/>
<variable initial_value="0.00650021800818712" name="C_s_O2" public_interface="out" units="mole_per_litre"/>
<variable initial_value="0.0219998602780634" name="C_s_CO2" public_interface="out" units="mole_per_litre"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_s_O2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>C_b_O2_init</ci>
<ci>C_s_O2</ci>
</apply>
<ci>tau_sys</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>C_s_CO2</ci>
</apply>
<apply>
<divide/>
<apply>
<minus/>
<ci>C_b_CO2_init</ci>
<ci>C_s_CO2</ci>
</apply>
<ci>tau_sys</ci>
</apply>
</apply>
</math>
</component>
<component name="acinus_compartment_1">
<variable name="time" public_interface="in" units="second"/>
<variable name="f_obs" public_interface="in" units="dimensionless"/>
<variable name="k_ex_O2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="k_ex_CO2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="V0" public_interface="in" units="metre_cubed"/>
<variable name="C_in_O2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="C_in_CO2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="P_atm_effective" public_interface="in" units="pascal"/>
<variable name="Q_blood_total" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_A" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_b" public_interface="in" units="m_cubed_per_s"/>
<variable name="P_b_O2" public_interface="in" units="pascal"/>
<variable name="P_b_CO2" public_interface="in" units="pascal"/>
<variable initial_value="0.000124080704592538" name="V_A" public_interface="out" units="metre_cubed"/>
<variable initial_value="2.60559105042863e-05" name="n_O2" public_interface="out" units="mole"/>
<variable initial_value="5.0293901179384e-08" name="n_CO2" public_interface="out" units="mole"/>
<variable name="P_A_O2" public_interface="out" units="pascal"/>
<variable name="I_ex_O2" public_interface="out" units="mole_per_second"/>
<variable name="I_ex_CO2" public_interface="out" units="mole_per_second"/>
<variable name="C_A_O2" units="mole_per_m_cubed"/>
<variable name="C_A_CO2" units="mole_per_m_cubed"/>
<variable name="P_A_CO2" units="pascal"/>
<variable name="G_O2" units="mol_per_Pa_s"/>
<variable name="G_CO2" units="mol_per_Pa_s"/>
<variable name="I_vent_O2" units="mole_per_second"/>
<variable name="I_vent_CO2" units="mole_per_second"/>
<variable name="dV_A_dt" units="m_cubed_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C_A_O2</ci>
<apply>
<divide/>
<ci>n_O2</ci>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_A_CO2</ci>
<apply>
<divide/>
<ci>n_CO2</ci>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_O2</ci>
<apply>
<times/>
<ci>C_A_O2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_CO2</ci>
<apply>
<times/>
<ci>C_A_CO2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>G_O2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_O2</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs</ci>
</apply>
<ci>V_A</ci>
<ci>Q_b</ci>
</apply>
<ci>Q_blood_total</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>G_CO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_CO2</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs</ci>
</apply>
<ci>V_A</ci>
<ci>Q_b</ci>
</apply>
<ci>Q_blood_total</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_ex_O2</ci>
<apply>
<times/>
<ci>G_O2</ci>
<apply>
<minus/>
<ci>P_A_O2</ci>
<ci>P_b_O2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_ex_CO2</ci>
<apply>
<times/>
<ci>G_CO2</ci>
<apply>
<minus/>
<ci>P_b_CO2</ci>
<ci>P_A_CO2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_vent_O2</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_O2</ci>
</apply>
<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_A_O2</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>I_vent_CO2</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_CO2</ci>
</apply>
<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_A_CO2</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>dV_A_dt</ci>
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<piece>
<cn cellml:units="m_cubed_per_s">0</cn>
<apply>
<and/>
<apply>
<leq/>
<ci>V_A</ci>
<ci>V0</ci>
</apply>
<apply>
<lt/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</apply>
</piece>
<otherwise>
<ci>Q_A</ci>
</otherwise>
</piecewise>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V_A</ci>
</apply>
<ci>dV_A_dt</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_O2</ci>
</apply>
<apply>
<minus/>
<ci>I_vent_O2</ci>
<ci>I_ex_O2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_CO2</ci>
</apply>
<apply>
<plus/>
<ci>I_vent_CO2</ci>
<ci>I_ex_CO2</ci>
</apply>
</apply>
</math>
</component>
<component name="acinus_compartment_2">
<variable name="time" public_interface="in" units="second"/>
<variable name="f_obs" public_interface="in" units="dimensionless"/>
<variable name="k_ex_O2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="k_ex_CO2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="V0" public_interface="in" units="metre_cubed"/>
<variable name="C_in_O2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="C_in_CO2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="P_atm_effective" public_interface="in" units="pascal"/>
<variable name="Q_blood_total" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_A" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_b" public_interface="in" units="m_cubed_per_s"/>
<variable name="P_b_O2" public_interface="in" units="pascal"/>
<variable name="P_b_CO2" public_interface="in" units="pascal"/>
<variable initial_value="0.000124080704592538" name="V_A" public_interface="out" units="metre_cubed"/>
<variable initial_value="2.60559105042309e-05" name="n_O2" public_interface="out" units="mole"/>
<variable initial_value="5.02939011790974e-08" name="n_CO2" public_interface="out" units="mole"/>
<variable name="P_A_O2" public_interface="out" units="pascal"/>
<variable name="I_ex_O2" public_interface="out" units="mole_per_second"/>
<variable name="I_ex_CO2" public_interface="out" units="mole_per_second"/>
<variable name="C_A_O2" units="mole_per_m_cubed"/>
<variable name="C_A_CO2" units="mole_per_m_cubed"/>
<variable name="P_A_CO2" units="pascal"/>
<variable name="G_O2" units="mol_per_Pa_s"/>
<variable name="G_CO2" units="mol_per_Pa_s"/>
<variable name="I_vent_O2" units="mole_per_second"/>
<variable name="I_vent_CO2" units="mole_per_second"/>
<variable name="dV_A_dt" units="m_cubed_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C_A_O2</ci>
<apply>
<divide/>
<ci>n_O2</ci>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_A_CO2</ci>
<apply>
<divide/>
<ci>n_CO2</ci>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_O2</ci>
<apply>
<times/>
<ci>C_A_O2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_CO2</ci>
<apply>
<times/>
<ci>C_A_CO2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>G_O2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_O2</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs</ci>
</apply>
<ci>V_A</ci>
<ci>Q_b</ci>
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<ci>Q_blood_total</ci>
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</apply>
<apply>
<eq/>
<ci>G_CO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_CO2</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs</ci>
</apply>
<ci>V_A</ci>
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<ci>Q_blood_total</ci>
</apply>
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<apply>
<eq/>
<ci>I_ex_O2</ci>
<apply>
<times/>
<ci>G_O2</ci>
<apply>
<minus/>
<ci>P_A_O2</ci>
<ci>P_b_O2</ci>
</apply>
</apply>
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<apply>
<eq/>
<ci>I_ex_CO2</ci>
<apply>
<times/>
<ci>G_CO2</ci>
<apply>
<minus/>
<ci>P_b_CO2</ci>
<ci>P_A_CO2</ci>
</apply>
</apply>
</apply>
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<eq/>
<ci>I_vent_O2</ci>
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<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_O2</ci>
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<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
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<times/>
<ci>Q_A</ci>
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</apply>
</otherwise>
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<apply>
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<ci>I_vent_CO2</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_CO2</ci>
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<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
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<apply>
<times/>
<ci>Q_A</ci>
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</otherwise>
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<apply>
<eq/>
<ci>dV_A_dt</ci>
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<piece>
<cn cellml:units="m_cubed_per_s">0</cn>
<apply>
<and/>
<apply>
<leq/>
<ci>V_A</ci>
<ci>V0</ci>
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<apply>
<lt/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
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</apply>
</piece>
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<ci>Q_A</ci>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
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<ci>dV_A_dt</ci>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_O2</ci>
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<apply>
<minus/>
<ci>I_vent_O2</ci>
<ci>I_ex_O2</ci>
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</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_CO2</ci>
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<apply>
<plus/>
<ci>I_vent_CO2</ci>
<ci>I_ex_CO2</ci>
</apply>
</apply>
</math>
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<component name="acinus_compartment_3">
<variable name="time" public_interface="in" units="second"/>
<variable name="f_obs" public_interface="in" units="dimensionless"/>
<variable name="k_ex_O2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="k_ex_CO2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="V0" public_interface="in" units="metre_cubed"/>
<variable name="C_in_O2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="C_in_CO2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="P_atm_effective" public_interface="in" units="pascal"/>
<variable name="Q_blood_total" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_A" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_b" public_interface="in" units="m_cubed_per_s"/>
<variable name="P_b_O2" public_interface="in" units="pascal"/>
<variable name="P_b_CO2" public_interface="in" units="pascal"/>
<variable initial_value="0.000124080704592538" name="V_A" public_interface="out" units="metre_cubed"/>
<variable initial_value="2.60559105041242e-05" name="n_O2" public_interface="out" units="mole"/>
<variable initial_value="5.02939011790014e-08" name="n_CO2" public_interface="out" units="mole"/>
<variable name="P_A_O2" public_interface="out" units="pascal"/>
<variable name="I_ex_O2" public_interface="out" units="mole_per_second"/>
<variable name="I_ex_CO2" public_interface="out" units="mole_per_second"/>
<variable name="C_A_O2" units="mole_per_m_cubed"/>
<variable name="C_A_CO2" units="mole_per_m_cubed"/>
<variable name="P_A_CO2" units="pascal"/>
<variable name="G_O2" units="mol_per_Pa_s"/>
<variable name="G_CO2" units="mol_per_Pa_s"/>
<variable name="I_vent_O2" units="mole_per_second"/>
<variable name="I_vent_CO2" units="mole_per_second"/>
<variable name="dV_A_dt" units="m_cubed_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C_A_O2</ci>
<apply>
<divide/>
<ci>n_O2</ci>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_A_CO2</ci>
<apply>
<divide/>
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<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_O2</ci>
<apply>
<times/>
<ci>C_A_O2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_CO2</ci>
<apply>
<times/>
<ci>C_A_CO2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>G_O2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_O2</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs</ci>
</apply>
<ci>V_A</ci>
<ci>Q_b</ci>
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<ci>Q_blood_total</ci>
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</apply>
<apply>
<eq/>
<ci>G_CO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_CO2</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs</ci>
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<ci>V_A</ci>
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<ci>Q_blood_total</ci>
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</apply>
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<eq/>
<ci>I_ex_O2</ci>
<apply>
<times/>
<ci>G_O2</ci>
<apply>
<minus/>
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<ci>P_b_O2</ci>
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</apply>
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<ci>I_ex_CO2</ci>
<apply>
<times/>
<ci>G_CO2</ci>
<apply>
<minus/>
<ci>P_b_CO2</ci>
<ci>P_A_CO2</ci>
</apply>
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<eq/>
<ci>I_vent_O2</ci>
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<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_O2</ci>
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<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
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<apply>
<times/>
<ci>Q_A</ci>
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</apply>
</otherwise>
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<apply>
<eq/>
<ci>I_vent_CO2</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_CO2</ci>
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<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
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<apply>
<times/>
<ci>Q_A</ci>
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</otherwise>
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<ci>dV_A_dt</ci>
<piecewise>
<piece>
<cn cellml:units="m_cubed_per_s">0</cn>
<apply>
<and/>
<apply>
<leq/>
<ci>V_A</ci>
<ci>V0</ci>
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<apply>
<lt/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
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</apply>
</piece>
<otherwise>
<ci>Q_A</ci>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
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<ci>dV_A_dt</ci>
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<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_O2</ci>
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<apply>
<minus/>
<ci>I_vent_O2</ci>
<ci>I_ex_O2</ci>
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</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_CO2</ci>
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<apply>
<plus/>
<ci>I_vent_CO2</ci>
<ci>I_ex_CO2</ci>
</apply>
</apply>
</math>
</component>
<component name="acinus_compartment_4">
<variable name="time" public_interface="in" units="second"/>
<variable name="f_obs" public_interface="in" units="dimensionless"/>
<variable name="k_ex_O2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="k_ex_CO2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="V0" public_interface="in" units="metre_cubed"/>
<variable name="C_in_O2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="C_in_CO2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="P_atm_effective" public_interface="in" units="pascal"/>
<variable name="Q_blood_total" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_A" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_b" public_interface="in" units="m_cubed_per_s"/>
<variable name="P_b_O2" public_interface="in" units="pascal"/>
<variable name="P_b_CO2" public_interface="in" units="pascal"/>
<variable initial_value="0.000124080704592538" name="V_A" public_interface="out" units="metre_cubed"/>
<variable initial_value="2.60559105046836e-05" name="n_O2" public_interface="out" units="mole"/>
<variable initial_value="5.02939011793512e-08" name="n_CO2" public_interface="out" units="mole"/>
<variable name="P_A_O2" public_interface="out" units="pascal"/>
<variable name="I_ex_O2" public_interface="out" units="mole_per_second"/>
<variable name="I_ex_CO2" public_interface="out" units="mole_per_second"/>
<variable name="C_A_O2" units="mole_per_m_cubed"/>
<variable name="C_A_CO2" units="mole_per_m_cubed"/>
<variable name="P_A_CO2" units="pascal"/>
<variable name="G_O2" units="mol_per_Pa_s"/>
<variable name="G_CO2" units="mol_per_Pa_s"/>
<variable name="I_vent_O2" units="mole_per_second"/>
<variable name="I_vent_CO2" units="mole_per_second"/>
<variable name="dV_A_dt" units="m_cubed_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C_A_O2</ci>
<apply>
<divide/>
<ci>n_O2</ci>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_A_CO2</ci>
<apply>
<divide/>
<ci>n_CO2</ci>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_O2</ci>
<apply>
<times/>
<ci>C_A_O2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_CO2</ci>
<apply>
<times/>
<ci>C_A_CO2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>G_O2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_O2</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs</ci>
</apply>
<ci>V_A</ci>
<ci>Q_b</ci>
</apply>
<ci>Q_blood_total</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>G_CO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_CO2</ci>
<apply>
<minus/>
<cn cellml:units="dimensionless">1</cn>
<ci>f_obs</ci>
</apply>
<ci>V_A</ci>
<ci>Q_b</ci>
</apply>
<ci>Q_blood_total</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_ex_O2</ci>
<apply>
<times/>
<ci>G_O2</ci>
<apply>
<minus/>
<ci>P_A_O2</ci>
<ci>P_b_O2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_ex_CO2</ci>
<apply>
<times/>
<ci>G_CO2</ci>
<apply>
<minus/>
<ci>P_b_CO2</ci>
<ci>P_A_CO2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_vent_O2</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_O2</ci>
</apply>
<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_A_O2</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>I_vent_CO2</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_CO2</ci>
</apply>
<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_A_CO2</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>dV_A_dt</ci>
<piecewise>
<piece>
<cn cellml:units="m_cubed_per_s">0</cn>
<apply>
<and/>
<apply>
<leq/>
<ci>V_A</ci>
<ci>V0</ci>
</apply>
<apply>
<lt/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</apply>
</piece>
<otherwise>
<ci>Q_A</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V_A</ci>
</apply>
<ci>dV_A_dt</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_O2</ci>
</apply>
<apply>
<minus/>
<ci>I_vent_O2</ci>
<ci>I_ex_O2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_CO2</ci>
</apply>
<apply>
<plus/>
<ci>I_vent_CO2</ci>
<ci>I_ex_CO2</ci>
</apply>
</apply>
</math>
</component>
<component name="acinus_compartment_5">
<variable name="time" public_interface="in" units="second"/>
<variable name="f_obs" public_interface="in" units="dimensionless"/>
<variable name="k_ex_O2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="k_ex_CO2" public_interface="in" units="mol_per_Pa_s"/>
<variable name="V0" public_interface="in" units="metre_cubed"/>
<variable name="C_in_O2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="C_in_CO2" public_interface="in" units="mole_per_m_cubed"/>
<variable name="P_atm_effective" public_interface="in" units="pascal"/>
<variable name="Q_blood_total" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_A" public_interface="in" units="m_cubed_per_s"/>
<variable name="Q_b" public_interface="in" units="m_cubed_per_s"/>
<variable name="P_b_O2" public_interface="in" units="pascal"/>
<variable name="P_b_CO2" public_interface="in" units="pascal"/>
<variable initial_value="0.000124080704592538" name="V_A" public_interface="out" units="metre_cubed"/>
<variable initial_value="2.60559105046743e-05" name="n_O2" public_interface="out" units="mole"/>
<variable initial_value="5.02939011791637e-08" name="n_CO2" public_interface="out" units="mole"/>
<variable name="P_A_O2" public_interface="out" units="pascal"/>
<variable name="I_ex_O2" public_interface="out" units="mole_per_second"/>
<variable name="I_ex_CO2" public_interface="out" units="mole_per_second"/>
<variable name="C_A_O2" units="mole_per_m_cubed"/>
<variable name="C_A_CO2" units="mole_per_m_cubed"/>
<variable name="P_A_CO2" units="pascal"/>
<variable name="G_O2" units="mol_per_Pa_s"/>
<variable name="G_CO2" units="mol_per_Pa_s"/>
<variable name="I_vent_O2" units="mole_per_second"/>
<variable name="I_vent_CO2" units="mole_per_second"/>
<variable name="dV_A_dt" units="m_cubed_per_s"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>C_A_O2</ci>
<apply>
<divide/>
<ci>n_O2</ci>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>C_A_CO2</ci>
<apply>
<divide/>
<ci>n_CO2</ci>
<ci>V_A</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_O2</ci>
<apply>
<times/>
<ci>C_A_O2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>P_A_CO2</ci>
<apply>
<times/>
<ci>C_A_CO2</ci>
<ci>P_atm_effective</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>G_O2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_O2</ci>
<apply>
<minus/>
<cn cellml:units="m_cubed_per_s">1</cn>
<ci>f_obs</ci>
</apply>
<ci>V_A</ci>
<ci>Q_b</ci>
</apply>
<ci>Q_blood_total</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>G_CO2</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>k_ex_CO2</ci>
<apply>
<minus/>
<cn cellml:units="m_cubed_per_s">1</cn>
<ci>f_obs</ci>
</apply>
<ci>V_A</ci>
<ci>Q_b</ci>
</apply>
<ci>Q_blood_total</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>I_ex_O2</ci>
<apply>
<times/>
<ci>G_O2</ci>
<apply>
<minus/>
<ci>P_A_O2</ci>
<ci>P_b_O2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_ex_CO2</ci>
<apply>
<times/>
<ci>G_CO2</ci>
<apply>
<minus/>
<ci>P_b_CO2</ci>
<ci>P_A_CO2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>I_vent_O2</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_O2</ci>
</apply>
<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_A_O2</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>I_vent_CO2</ci>
<piecewise>
<piece>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_in_CO2</ci>
</apply>
<apply>
<geq/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</piece>
<otherwise>
<apply>
<times/>
<ci>Q_A</ci>
<ci>C_A_CO2</ci>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>dV_A_dt</ci>
<piecewise>
<piece>
<cn cellml:units="m_cubed_per_s">0</cn>
<apply>
<and/>
<apply>
<leq/>
<ci>V_A</ci>
<ci>V0</ci>
</apply>
<apply>
<lt/>
<ci>Q_A</ci>
<cn cellml:units="m_cubed_per_s">0</cn>
</apply>
</apply>
</piece>
<otherwise>
<ci>Q_A</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V_A</ci>
</apply>
<ci>dV_A_dt</ci>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_O2</ci>
</apply>
<apply>
<minus/>
<ci>I_vent_O2</ci>
<ci>I_ex_O2</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>n_CO2</ci>
</apply>
<apply>
<plus/>
<ci>I_vent_CO2</ci>
<ci>I_ex_CO2</ci>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="Environment">
<component_ref component="breathing_waveform"/>
<component_ref component="ventilation_distributor"/>
<component_ref component="perfusion_distributor"/>
<component_ref component="pulmonary_blood_pool"/>
<component_ref component="systemic_circulation"/>
<component_ref component="acinus_compartment_1"/>
<component_ref component="acinus_compartment_2"/>
<component_ref component="acinus_compartment_3"/>
<component_ref component="acinus_compartment_4"/>
<component_ref component="acinus_compartment_5"/>
</component_ref>
</group>
<connection>
<map_components component_1="Environment" component_2="breathing_waveform"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="pulmonary_blood_pool"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="P_atm_effective" variable_2="P_atm_effective"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="systemic_circulation"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="breathing_waveform" component_2="ventilation_distributor"/>
<map_variables variable_1="Q_vent_total" variable_2="Q_vent_total"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="acinus_compartment_1"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="P_atm_effective" variable_2="P_atm_effective"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="acinus_compartment_2"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="P_atm_effective" variable_2="P_atm_effective"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="acinus_compartment_3"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="P_atm_effective" variable_2="P_atm_effective"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="acinus_compartment_4"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="P_atm_effective" variable_2="P_atm_effective"/>
</connection>
<connection>
<map_components component_1="Environment" component_2="acinus_compartment_5"/>
<map_variables variable_1="time" variable_2="time"/>
<map_variables variable_1="P_atm_effective" variable_2="P_atm_effective"/>
</connection>
<connection>
<map_components component_1="ventilation_distributor" component_2="acinus_compartment_1"/>
<map_variables variable_1="Q_A_1" variable_2="Q_A"/>
<map_variables variable_1="V0_1" variable_2="V0"/>
<map_variables variable_1="f_obs_1" variable_2="f_obs"/>
<map_variables variable_1="C_in_O2" variable_2="C_in_O2"/>
<map_variables variable_1="C_in_CO2" variable_2="C_in_CO2"/>
</connection>
<connection>
<map_components component_1="ventilation_distributor" component_2="acinus_compartment_2"/>
<map_variables variable_1="Q_A_2" variable_2="Q_A"/>
<map_variables variable_1="V0_2" variable_2="V0"/>
<map_variables variable_1="f_obs_2" variable_2="f_obs"/>
<map_variables variable_1="C_in_O2" variable_2="C_in_O2"/>
<map_variables variable_1="C_in_CO2" variable_2="C_in_CO2"/>
</connection>
<connection>
<map_components component_1="ventilation_distributor" component_2="acinus_compartment_3"/>
<map_variables variable_1="Q_A_3" variable_2="Q_A"/>
<map_variables variable_1="V0_3" variable_2="V0"/>
<map_variables variable_1="f_obs_3" variable_2="f_obs"/>
<map_variables variable_1="C_in_O2" variable_2="C_in_O2"/>
<map_variables variable_1="C_in_CO2" variable_2="C_in_CO2"/>
</connection>
<connection>
<map_components component_1="ventilation_distributor" component_2="acinus_compartment_4"/>
<map_variables variable_1="Q_A_4" variable_2="Q_A"/>
<map_variables variable_1="V0_4" variable_2="V0"/>
<map_variables variable_1="f_obs_4" variable_2="f_obs"/>
<map_variables variable_1="C_in_O2" variable_2="C_in_O2"/>
<map_variables variable_1="C_in_CO2" variable_2="C_in_CO2"/>
</connection>
<connection>
<map_components component_1="ventilation_distributor" component_2="acinus_compartment_5"/>
<map_variables variable_1="Q_A_5" variable_2="Q_A"/>
<map_variables variable_1="V0_5" variable_2="V0"/>
<map_variables variable_1="f_obs_5" variable_2="f_obs"/>
<map_variables variable_1="C_in_O2" variable_2="C_in_O2"/>
<map_variables variable_1="C_in_CO2" variable_2="C_in_CO2"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_1"/>
<map_variables variable_1="Q_b_1" variable_2="Q_b"/>
<map_variables variable_1="k_ex_O2_1" variable_2="k_ex_O2"/>
<map_variables variable_1="k_ex_CO2_1" variable_2="k_ex_CO2"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_2"/>
<map_variables variable_1="Q_b_2" variable_2="Q_b"/>
<map_variables variable_1="k_ex_O2_2" variable_2="k_ex_O2"/>
<map_variables variable_1="k_ex_CO2_2" variable_2="k_ex_CO2"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_3"/>
<map_variables variable_1="Q_b_3" variable_2="Q_b"/>
<map_variables variable_1="k_ex_O2_3" variable_2="k_ex_O2"/>
<map_variables variable_1="k_ex_CO2_3" variable_2="k_ex_CO2"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_4"/>
<map_variables variable_1="Q_b_4" variable_2="Q_b"/>
<map_variables variable_1="k_ex_O2_4" variable_2="k_ex_O2"/>
<map_variables variable_1="k_ex_CO2_4" variable_2="k_ex_CO2"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_5"/>
<map_variables variable_1="Q_b_5" variable_2="Q_b"/>
<map_variables variable_1="k_ex_O2_5" variable_2="k_ex_O2"/>
<map_variables variable_1="k_ex_CO2_5" variable_2="k_ex_CO2"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="pulmonary_blood_pool"/>
<map_variables variable_1="Q_blood_total" variable_2="Q_blood_total"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_1"/>
<map_variables variable_1="Q_blood_total" variable_2="Q_blood_total"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_2"/>
<map_variables variable_1="Q_blood_total" variable_2="Q_blood_total"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_3"/>
<map_variables variable_1="Q_blood_total" variable_2="Q_blood_total"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_4"/>
<map_variables variable_1="Q_blood_total" variable_2="Q_blood_total"/>
</connection>
<connection>
<map_components component_1="perfusion_distributor" component_2="acinus_compartment_5"/>
<map_variables variable_1="Q_blood_total" variable_2="Q_blood_total"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_1" component_2="perfusion_distributor"/>
<map_variables variable_1="P_A_O2" variable_2="P_A_O2_1"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_2" component_2="perfusion_distributor"/>
<map_variables variable_1="P_A_O2" variable_2="P_A_O2_2"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_3" component_2="perfusion_distributor"/>
<map_variables variable_1="P_A_O2" variable_2="P_A_O2_3"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_4" component_2="perfusion_distributor"/>
<map_variables variable_1="P_A_O2" variable_2="P_A_O2_4"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_5" component_2="perfusion_distributor"/>
<map_variables variable_1="P_A_O2" variable_2="P_A_O2_5"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_1" component_2="pulmonary_blood_pool"/>
<map_variables variable_1="I_ex_O2" variable_2="I_ex_O2_1"/>
<map_variables variable_1="I_ex_CO2" variable_2="I_ex_CO2_1"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_2" component_2="pulmonary_blood_pool"/>
<map_variables variable_1="I_ex_O2" variable_2="I_ex_O2_2"/>
<map_variables variable_1="I_ex_CO2" variable_2="I_ex_CO2_2"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_3" component_2="pulmonary_blood_pool"/>
<map_variables variable_1="I_ex_O2" variable_2="I_ex_O2_3"/>
<map_variables variable_1="I_ex_CO2" variable_2="I_ex_CO2_3"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_4" component_2="pulmonary_blood_pool"/>
<map_variables variable_1="I_ex_O2" variable_2="I_ex_O2_4"/>
<map_variables variable_1="I_ex_CO2" variable_2="I_ex_CO2_4"/>
</connection>
<connection>
<map_components component_1="acinus_compartment_5" component_2="pulmonary_blood_pool"/>
<map_variables variable_1="I_ex_O2" variable_2="I_ex_O2_5"/>
<map_variables variable_1="I_ex_CO2" variable_2="I_ex_CO2_5"/>
</connection>
<connection>
<map_components component_1="pulmonary_blood_pool" component_2="acinus_compartment_1"/>
<map_variables variable_1="P_b_O2" variable_2="P_b_O2"/>
<map_variables variable_1="P_b_CO2" variable_2="P_b_CO2"/>
</connection>
<connection>
<map_components component_1="pulmonary_blood_pool" component_2="acinus_compartment_2"/>
<map_variables variable_1="P_b_O2" variable_2="P_b_O2"/>
<map_variables variable_1="P_b_CO2" variable_2="P_b_CO2"/>
</connection>
<connection>
<map_components component_1="pulmonary_blood_pool" component_2="acinus_compartment_3"/>
<map_variables variable_1="P_b_O2" variable_2="P_b_O2"/>
<map_variables variable_1="P_b_CO2" variable_2="P_b_CO2"/>
</connection>
<connection>
<map_components component_1="pulmonary_blood_pool" component_2="acinus_compartment_4"/>
<map_variables variable_1="P_b_O2" variable_2="P_b_O2"/>
<map_variables variable_1="P_b_CO2" variable_2="P_b_CO2"/>
</connection>
<connection>
<map_components component_1="pulmonary_blood_pool" component_2="acinus_compartment_5"/>
<map_variables variable_1="P_b_O2" variable_2="P_b_O2"/>
<map_variables variable_1="P_b_CO2" variable_2="P_b_CO2"/>
</connection>
<connection>
<map_components component_1="pulmonary_blood_pool" component_2="systemic_circulation"/>
<map_variables variable_1="C_sys_O2" variable_2="C_s_O2"/>
<map_variables variable_1="C_sys_CO2" variable_2="C_s_CO2"/>
<map_variables variable_1="C_b_O2" variable_2="C_b_O2_init"/>
<map_variables variable_1="C_b_CO2" variable_2="C_b_CO2_init"/>
</connection>
</model>
